Great rhombitrihexagonal tiling
Jump to navigation
Jump to search
| Great rhombitrihexagonal tiling | |
|---|---|
 | |
| Rank | 3 |
| Type | Uniform |
| Space | Euclidean |
| Notation | |
| Bowers style acronym | Grothat |
| Coxeter diagram | x6x3x (   ) |
| Elements | |
| Faces | 3N Squares, 2N hexagons, N dodecagons |
| Edges | 6N+6N+6N |
| Vertices | 12N |
| Vertex figure | Scalene triangle, edge lengths √2, √3, (√2+√6)/2 |
| Measures (edge length 1) | |
| Vertex density | |
| Related polytopes | |
| Army | Grothat |
| Regiment | Grothat |
| Dual | Kisrhombille tiling |
| Conjugate | Quasitruncated trihexagonal tiling |
| Abstract & topological properties | |
| Flag count | 72N |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | V3 |
| Convex | Yes |
| Nature | Tame |
The great rhombitrihexagonal tiling, or grothat, also called the omnitruncated trihexagonal tiling, or othat, is one of the eleven convex uniform tilings of the Euclidean plane. 1 square, 1 hexagon, and 1 dodecagon join at each vertex of this tiling. As its name suggests, it is the omnitruncate of the V3 family of Euclidean tilings.
External links[edit | edit source]
- Klitzing, Richard. "grothat".
- Wikipedia contributors. "Truncated trihexagonal tiling".
 truncations | ||||
|---|---|---|---|---|
| Name | OBSA | Schläfli symbol | CD diagram | Image |
| Hexagonal tiling | hexat | {6,3} | |  |
| Trihexagonal tiling | that | r {6,3} | |  |
| Triangular tiling | trat | {3,6} | |  |
| Truncated hexagonal tiling | toxat | t {6,3} | |  |
| Small rhombitrihexagonal tiling | srothat | rr {6,3} | |  |
| Truncated triangular tiling = Hexagonal tiling | hexat | t {3,6} | |  |
| Great rhombitrihexagonal tiling | grothat | tr {6,3} | |  |
| Snub trihexagonal tiling | snathat | sr {6,3} |  |  |